In this paper, we investigate the capacity distribution of spatially correlated, multiple-input-multiple-output (MIMO) channels. In particular, we derive a concise closed-form expression for the characteristic function (c.f.) of MIMO system capacity with arbitrary correlation among the transmitting antennas or among the receiving antennas in frequency-flat Rayleigh-fading environments. Using the exact expression of the c.f., the probability density function (pdf) and the cumulative distribution function (CDF) can be easily obtained, thus enabling the exact evaluation of the outage and mean capacity of spatially correlated MIMO channels. Our results are valid for scenarios with the number of transmitting antennas greater than or equal to that of receiving antennas with arbitrary correlation among them. Moreover, the results are valid for an arbitrary number of transmitting and receiving antennas in uncorrelated MIMO channels. It is shown that the capacity loss is negligible even with a correlation coefficient between two adjacent antennas as large as 0.5 for exponential correlation model. Finally, we derive an exact expression for the mean value of the capacity for arbitrary correlation matrices. View full abstract»

Fading MIMO relay channels are studied analytically, when the source and destination are equipped with multiple antennas and the relays have a single one. Compact closed-form expressions are obtained for the outage probability under i.i.d. and correlated Rayleigh-fading links. Low-outage approximations are derived, which reveal a number of insights, including the impact of correlation, of the number of antennas, of relay noise and of relaying protocol. The effect of correlation is shown to be negligible, unless the channel becomes almost fully correlated. The SNR loss of relay fading channels compared to the AWGN channel is quantified. The SNR-asymptotic diversity-multiplexing tradeoff (DMT) is obtained for a broad class of fading distributions, including, as special cases, Rayleigh, Rice, Nakagami, Weibull, which may be non-identical, spatially correlated and/or non-zero mean. The DMT is shown to depend not on a particular fading distribution, but rather on its polynomial behavior near zero, and is the same for the simple "amplify-and-forward" protocol and more complicated "decode-and-forward" one with capacity achieving codes, i.e. the full processing capability at the relay does not help to improve the DMT. There is however a significant difference between the SNR-asymptotic DMT and the finite-SNR outage performance: while the former is not improved by using an extra antenna on either side, the latter can be significantly improved and, in particular, an extra antenna can be traded-off for a full processing capability at the relay. The results are extended to the multi-relay channels with selection relaying and typical outage events are identified. View full abstract»

MIMO systems exploit the multipath propagation in rich scattering environment using multiple transmit and receive antennas to increase the capacity of a link. The matrix channel plays a pivotal role in the throughput of a MIMO link since the modulation, data rate, power allocation and antenna weights are dependent on the channel gain. This paper evaluates adaptively modulated open loop MIMO system with limited feedback and adaptively modulated closed loop MIMO systems. For open loop MIMO a modified V-BLAST system with limited feedback is considered. This is compared with a rate maximization algorithm for closed loop MIMO using iid flat-fading Rayleigh channel, spatially correlated channel and realistic indoor channel. It is shown that when realistic models are used the difference in performance between closed loop MIMO and limited feedback V-BLAST systems is greater. At a noise-normalized power of 25 dB the percentage improvement in the throughput of CL-MIMO over OL-MIMO is 15.1% for Rayleigh fading channel, 48.1% for the spatially correlated channel and 104% for the realistic channel model. It is also shown that the throughput reduces in presence of channel correlation and that this affects the performance of the limited feedback V-BLAST system to a greater extent in comparison with CL-MIMO system. The average SNR penalty for OL-MIMO to achieve same throughput as CL-MlMO is 4dB for the Rayleigh fading model, 7dB for the spatially correlated model and 10 dB for the realistic channel model. View full abstract»

Recently, we reported a low-complexity likelihood ascent search (LAS) detection algorithm for large MIMO systems with several tens of antennas that can achieve high spectral efficiencies of the order of tens to hundreds of bps/Hz. Through simulations, we showed that this algorithm achieves increasingly near SISO AWGN performance for increasing number of antennas in i.i.d. Rayleigh fading. However, no bit error performance analysis of the algorithm was reported. In this paper, we extend our work on this low-complexity large MIMO detector in two directions: i)We report an asymptotic bit error probability analysis of the LAS algorithm in the large system limit, where N_t, N_r rarr infin keeping N_t = N_r, where N_t and N_r are the number of transmit and receive antennas, respectively. Specifically, we prove that the error performance of the LAS detector for V-BLAST with 4-QAM in i.i.d. Rayleigh fading converges to that of the maximum-likelihood (ML) detector as N_t,N_r rarr infin keeping N_t = N_r. ii)We present simulated BER and nearness to capacity results for V-BLAST as well as high-rate non-orthogonal STBC from Division Algebras (DA), in a more realistic spatially correlated MIMO channel model. Our simulation results show that a) at an uncoded BER of 10^-3, the performance of the LAS detector in decoding 16 times16 STBC from DA with N_t = N_r =16 and 16-QAM degrades in spatially correlated fading by about 7 dB compared to that in i.i.d. fading, and b) with a rate-3/4 outer turbo code and 48 bps/Hz spectral efficiency, the performance degrades by about 6 dB at a coded BER of 10^-4. Our results further show that providing asymmetry in number of antennas such that N_r > N_t keeping the total receiver array length same as that for N_r = N_t, the detector is able to pick up the extra recei- - ve diversity thereby significantly improving the BER performance. View full abstract»

We investigate the capacity distribution of spatially correlated MIMO channels. In particular, we consider MIMO systems with arbitrary correlation among the transmitting antennas or among the receiving antennas in frequency-flat Rayleigh fading environments. We derive a simple expression for the distribution of the eigenvalues of a Wishart matrix including correlation, and then a closed-form expression for the characteristic function (CF) of MIMO system capacity. Using the exact expression of the CF, the probability density function and the cumulative distribution function can be easily obtained, thus enabling the exact evaluation of the outage and mean capacity of spatially correlated MIMO channels. View full abstract»

We investigate the non-coherent single-user MIMO channel in the low signal-to-noise (SNR) regime from two viewpoints: capacity and probability of error analysis. The novelty in both viewpoints is that an arbitrary correlation structure is allowed for the Gaussian observation noise. First, we look at the capacity of the spatially correlated Rayleigh fading channel. We investigate the impact of channel and noise correlation on the mutual information for the on-off and Gaussian signaling schemes. Our results establish that, in the low SNR regime, mutual information is maximized when the transmit antennas are fully correlated (the same holds for the receive array). Then, we consider the deterministic channel setup and perform a pairwise error probability (PEP) analysis for the GLRT receiver. This leads to a codebook design criterion on which we base the construction of new space-time constellations. Their performance is assessed by computer simulations and, as a byproduct, we show that our codebooks are also of interest for Bayesian receivers which decode constellations with non-uniform priors View full abstract»

New results are presented for the ergodic capacity of spatially-correlated, time-varying and frequency-selective (i.e., triply selective) MIMO Rayleigh fading channels. Simplified capacity formulas are also derived for special cases such as SIMO and MISO triply selective fading channels. A closed form formula is proposed that quantifies the effect of the frequency-selective fading on the ergodic capacity into an intersymbol interference (ISI) degradation factor. It is discovered that, in general frequency-selective MIMO channels, the ISI inter-tap correlations reduce the ergodic capacity compared to the frequency flat fading channel. Only in the special case when the fading does not have ISI inter-tap correlations will the ergodic capacity be the same as that of the frequency flat channel. The new capacity results are experimentally verified via Monte-Carlo simulations. View full abstract»

The noncoherent single-user multiple-input-multiple-output (MIMO) channel in the low signal-to-noise ratio (SNR) regime is investigated from two viewpoints: capacity and probability of error analysis. The novelty in both viewpoints is that we allow an arbitrary correlation structure for the Gaussian observation noise. First, we look at the capacity of the spatially correlated Rayleigh fading channel. We investigate the impact of channel and noise correlation on the mutual information for the on-off and Gaussian signaling schemes. Our findings establish that, in the low SNR regime, mutual information is maximized when the transmit antennas are fully correlated (the same holds for the receive array). Then, the deterministic channel setup is considered and a pairwise error probability (PEP) analysis for the generalized likelihood ratio test (GLRT) receiver is performed. This leads to a codebook design criterion on which we base the construction of new space-time constellations. Their performance is assessed by computer simulations and, as a byproduct, we show that our codebooks are also of interest for Bayesian receivers, which decode constellations with nonuniform priors. View full abstract»

MIMO single-relay fading channels are studied, where the source and destination are equipped with multiple antennas and the relay has a single one. Compact closed-form expressions are obtained for the outage probability under i.i.d. and correlated Rayleigh-fading links. Insightful high-SNR approximations are derived, which show the impact of the number of antennas, correlation, relay noise, relaying protocol, etc. Diversity-multiplexing tradeoff (DMT) is obtained for a broad class of fading distributions, including, as special cases, Rayleigh, Rice, Nakagami, Weibull, which may be non-identical, spatially correlated and/or non-zero mean. The DMT is shown to depend not on a particular fading distribution, but rather on its polynomial behavior near zero. It turns out to be the same for the simple “amplify-and-forward” protocol and more complicated “decode-and-forward” one with capacity achieving codes, i.e. the full processing capability at the relay does not help to improve the DMT. However, we also emphasize significant difference between the SNR-asymptotic DMT and the finite-SNR outage performance: while the former is not improved by using an extra antenna on either side, the latter can be significantly improved and, in particular, an extra antenna can be traded-off for a full processing capability at the relay. View full abstract»

Amplify-and-Forward (AF) is a simple but effective relaying concept for multihop networks that combines transparency regarding modulation format and coding scheme with ease of implementation. Recently, a spatial filter design for MIMO AF relays was proposed that allows for capacity gains when having i.i.d. Rayleigh fading channels and full channel knowledge available at the relay station. In this paper, correlated MIMO channels are considered and spatial filter designs for partial channel knowledge at the relay station are considered. It appears that for correlated MIMO channels, it becomes essential to spatially filter the signal at the relay station in order to avoid implicit beamforming into wrong directions View full abstract»

We put forth a saddlepoint approximation for the outage capacity of multiple-input multiple-output (MIMO) systems using the exact moment generating function of the capacity. We consider both uncorrelated and spatially correlated Rayleigh-fading channels. Our results show that the saddlepoint method gives a remarkably accurate approximation to the outage capacity even at extremely low outage probabilities View full abstract»

Approximate closed-form density and distribution functions for the capacity of multiple-input multiple-output (MIMO) radio systems in spatially semi-correlated Rayleigh fading channels are derived. The approximations are given in terms of the Meijer G-function, hence allowing easy numerical evaluation of capacity outage probabilities with, for example, Maple or Mathematica. View full abstract»

We analyze a mobile multiple input multiple output wireless link with M transmit and N receive antennas operating in a spatially correlated Rayleigh flat fading environment. Only the correlations between the channel coefficients are assumed to be known at the transmitter and the receiver. The channel coefficients are correlated in space and uncorrelated in time from one coherence interval to another. These coefficients remain constant for a coherence interval of T symbol periods after which they change to another independent realization according to the spatial correlation model. For this system we characterize the structure of the input signal that achieves capacity. The capacity achieving transmit signal is expressed as the product of an isotropically distributed unitary matrix, an independent nonnegative diagonal matrix and a unitary matrix whose columns are the eigenvectors of the transmit fade covariance matrix. For the case where the number of transmit antennas M is larger than the channel coherence interval T, we show that the channel capacity is independent of the smallest M-T eigenvalues of the transmit fade covariance matrix. In contrast to the previously reported results for the spatially white fading model where adding more transmit antennas beyond the coherence interval length (M>T) does not increase capacity, we find that additional transmit antennas always increase capacity as long as their channel fading coefficients are spatially correlated with the other antennas. We show that for fast hopping or fast fading systems (T=1) with only channel covariance information available to the transmitter and receiver, transmit fade correlations are beneficial. Mathematically, we prove this by showing that capacity is a Schur-convex function of the vector of eigenvalues of the transmit fade correlation matrix. We also show that the maximum possible capacity gain due to transmitter fade correlations is 10logM dB. View full abstract»

The delay-limited capacity is defined as the transmission rate that can be guaranteed in all fading states under finite long-term power constraints. For the single-input single-output Rayleigh fading channel it is zero. In contrast it is greater than zero in multiple antenna channels but depends on the properties of the fading channel, e.g. on the spatial correlation. In this work, we prove that the delay-limited capacity is Schur-concave with respect to the spatial correlation. In addition to the average power constraint, we apply a peak-power constraint which limits the kurtosis of the input signal. We derive the delay-limited capacity for this general class of multiple antenna channels with correlation under peak-power and long-term power constraint. Without the stringent delay constraint, the maximum throughput is defined as the transmission rate times successful transmission probability. When the transmitter is uninformed, the maximum throughput is achieved for small SNR by using only one transmit antenna and for high SNR by using all available transmit antennas. When the transmitter has perfect channel knowledge, the optimal power allocation under long-term power constraint is analyzed and the impact of correlation is discussed by numerical simulations. View full abstract»

In this paper, the ergodic capacity of multiple antenna systems over spatially correlated Rayleigh-fading channels is investigated under the assumption that the channel state information (CSI) is unknown at the transmitter and perfectly known at the receiver. We derive a lower-bound expression, in closed form, for the ergodic capacity through the use of majorization theory and the probability density function (PDF) of the sum of Gamma random variables, which is represented by an infinite series. Furthermore, we also obtain other lower-bounds from the truncation of such series, and we associate truncation errors. Finally, the proposal of the paper is compared with a lower-bound reported in the literature. View full abstract»

Instead of using eigen-beamforming approach to increase capacity gain, an optimal pre-weighting scheme is employed in the closed-loop multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (MIMO-OFDM) wireless system design under subcarrier cluster constraint. This scheme adopts an uplink scale weight vector on the space-time block code (STBC) signals in accordance to its space-time constellation, without utilizing the transmit channel state information (TCSI). A Bayes decision algorithm is considered to generate the optimum weight vectors using channel coefficients measured from pilot subcarriers in each MIMO sub-channel. Analytical expressions of the signal-to-noise power ratio (SNR) improvement are derived over spatially correlated MIMO fading channels. Our Monte Carlo simulations show that the proposed scheme outperforms the Alamouti detection scheme in terms of the symbol-error-rate (SER) performance of 16QAM modulating with respect to various pilot intervals. The maximizing eigenvalue distributions (EVD) also validate our results. View full abstract»

In this paper, delay constrained performance of a multiple-input multiple-output (MIMO) communication system with orthogonal space-time block coding (OSTBC) at the transmitter is investigated. For alleviating the high complexity and cost of the MIMO system, receive antenna selection (RAS) scheme is employed here. We consider downlink channel where simple and cheap mobile switches are required. In this case, one antenna is chosen at the receiver. Moreover at the transmitter, in a perfect channel condition, there is no mutual coupling between transmit antennas. On the other hand, for a practical situation we assume spatial correlation between the transmit antennas. Under these assumptions, a maximum constant arrival rate with the delay quality-of-service (QoS) guarantee in a wireless channel is extracted. We obtain a closed-form solution for the effective capacity of the MIMO-OSTBC channel with the RAS scheme in a quasi-static Rayleigh fading conditions. Finally, the numerical simulations are provided and verified the theoretical results. View full abstract»

Instead of using eigen-beamforming approach to increase capacity gain, an optimal pre-weighting scheme is employed in the closed-loop multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (MIMO-OFDM) wireless system design under subcarrier cluster constraint. This scheme adopts an up-link scale weight vector on the space-time block code (STBC) signals in accordance to its space-time constellation, without utilizing the transmit channel state information (TCSI). Hence, a Bayes decision algorithm is considered to generate the optimum weight vectors using channel coefficients measured from pilot subcarriers in each MIMO sub-channel. Analytical expressions of the signal-to-noise power ratio (SNR) improvement are derived over spatially correlated MIMO fading channels. Inter-subcarrier-interference (ISI) caused by the Doppler effect was also taken into account to evaluate the channel robustness enhancement. Our Monte Carlo simulations show that the proposed scheme outperforms the Alamouti detection scheme in terms of the bit-error-rate (BER) performances of QPSK and 16QAM, respectively, with respect to various pilot intervals. The maximizing eigenvalue distributions (EVD) also validate our results. View full abstract»

For a block fading multiple input multiple output (MIMO) wireless link comprising M transmit and N receive antennas operating in a spatially correlated Rayleigh flat fading environment with coherence time T and only knowledge of channel correlations at the transmitter and receiver, we show that the channel capacity is independent of the smallest M-T eigenvalues of the transmit fade covariance matrix. We characterize the structure of the input signal that achieves capacity. In contrast to the previously reported results for the spatially white fading model where adding more transmit antennas beyond the coherence interval length (M>T) does not increase capacity, we find that additional transmit antennas always increase capacity as long as their channel fading coefficients are spatially correlated, making the case for smaller spacing between transmit antennas. For fast fading channels the capacity gained from multiple transmit antennas is bounded by the array gain 10 log M. View full abstract»

In this paper, we derive a closed form necessary and sufficient condition under which rank r multichannel beamforming achieves the capacity of a single user spatially correlated Rayleigh fading channel which employs multiple transmit antennas and a single receive antenna. It is assumed that the receiver has perfect channel side information (CSIR) while the transmitter only knows the channel distribution (CDIT). Additionally, a set of r independent closed form equation is derived that gives the r non-zero eigenvalues of transmit covariance associated to transmit power along each mode. View full abstract»

In this paper, we present a comprehensive analysis of the outage probability for multiple-input multiple-output (MIMO) systems over spatially correlated Rayleigh fading chan-nels. In our analysis, we assume that 1) the channel state information (CSI) is perfectly known at the receiver but not at the transmitter, 2) the spatial correlation is present at both ends of the wireless communications link, 3) the transmit and receive correlation matrices may or may not be full rank, and 4) the underlying channel is quasi-static fading. With these assumptions, we derive explicit bounds for the outage probability and show that the diversity order is simply the product of the rank of the transmit correlation matrix and the rank of the receive correlation matrix. We also derive an expression that accurately quantifies the degradation in the signal-to-noise ratio (SNR) due to the presence of correlation. We present several numerical examples that validate our analysis. View full abstract»

This paper presents a new spatially correlated Rayleigh fading channel generation technique for multiple-input-multiple-output (MIMO) systems via recently proposed virtual channel representation (VCR). In contrast to the traditional production correlated channel generation, the new VCR approach generates correlated channel via two dimensional discrete Fourier transform (DFT). This work extends the theoretical correlation coefficient results from single-input-multiple-output (SIMO) to MIMO channels. In addition, theoretically we show that the currently used production method is a special case of the new VCR technique, since the former considers only local scatterers, but the latter considers non-local scatterers as well. Hence, this work leads to the conclusion that VCR is a more general channel model compared with 2-D production-form. View full abstract»

We consider a receive antenna selection multiple-input-multiple-output (MIMO) system, where only one out of N _r receive antennas is selected. Spatial channel correlation will be considered at the receiver side only. Our goal is to investigate the capacity performance of this system. In particular, we will derive a closed-form expression for the outage probability and an upper bound for the ergodic (average) capacity. These quantities will be expressed using an infinite series representation. To do so, we will first derive the joint cumulative distribution function and the joint probability density function of the squared row norms of the channel matrix. This is enabled by taking advantage of the statistical properties of multivariate chi-squared random variables. Using the outage expression derived, we demonstrate that the considered antenna selection system achieves a full diversity order that is similar to a MIMO system without antenna selection. Next, we derive the probability density function of the maximum of the squared row norms of the channel matrix and its moments, which is straightly related to the system ergodic capacity. We also analyze the error rate performance of the aforementioned receive antenna selection MIMO system while using orthogonal space-time block codes (OSTBCs) at the transmitter. Our simulation results are shown to validate our analytical findings. View full abstract»

In this paper, we investigate the behaviors of the optimum end-to-end distortion of spatially correlated, multiple-input-multiple-output (MIMO) systems. Assuming Rayleigh fading channel and the transmitter perfectly knows the instantaneous channel rate, we derive an analytic expression of the tight lower bound of the end-to-end mean quadratic distortion at any SNR for transmitting a white thermal noise source, in terms of the spatial correlation matrix, antenna numbers, the ratio of source-bandwidth to channel-bandwidth, the ratio of signal power to noise power (SNR) and the source power. By analyzing the expression, we obtain the SNR exponent and the corresponding factor at the asymptotically high SNR. Also, we show that higher correlation brings higher distortion lower bound, which corresponds to our intuition. View full abstract»

In need for high-speed data transmission over wireless channels, multiple-input multiple-output (MIMO) technology has been suggested as it exhibits significant improvement in channel capacity. In practice, adaptive modulation scheme can be applied in different MIMO algorithms to further improve the system efficiency. In this paper, we derive closed-form expressions for the spectral efficiency of MIMO system utilizing two algorithms: Orthogonal Space-Time Block Coding (OSTBC) and spatial multiplexing with zero-forcing (ZF) receiver. Furthermore, a low-complexity adaptive scheme that switches between OSTBC and ZF to achieve even a higher spectral efficiency is suggested based on the closed form expressions. View full abstract»